Robust iterative learning for high precision motion control through L 1 adaptive feedback

Abstract The diversity of precision motion control applications and their demanding design specifications pose a large array of control challenges. Hence, precision motion control design relies on a variety of advanced control strategies developed to cope with specific problems present in control theory. A popular feedforward control technique for repetitive systems is iterative learning control (ILC). While ILC can decrease tracking errors up to several orders of magnitude, the achievable performance is limited by dynamic uncertainty. We propose the combination of L 1 adaptive control ( L 1 AC) and linear ILC for precision motion control under parametric uncertainties. We rely on the adaptive loop to compensate for parametric uncertainties, and ensure that the plant uncertainty is sufficiently small so that an aggressive learning controller can be designed on the nominal system. We exploit the closed loop stability condition of L 1 AC to design simple, robust ILC update laws that reduce tracking errors to measurement noise for time varying references and uncertainties. We demonstrate in simulation that the combined control scheme maintains a highly predictable, monotonic system behavior; and achieves near perfect tracking within a few trials regardless of the uncertainty present.